connected graph

K-edge-connected graph

In graph theory, a graph G with edge set E(G) is said to be k-edge-connected if G setminus X is connected for all X subseteq E(G) with left| X right| < k. In plain English, a graph is k-edge-connected if the graph remains connected when you delete fewer than k edges from the graph.

If a graph G is k-edge-connected then k le delta(G), where delta(G) is the minimum degree of any vertex v in V(G). This fact is clear since deleting all edges with an end at a vertex of minimum degree will disconnect that vertex from the graph.